The present invention relates to a process for producing a propylene-ethylene block copolymer having high rigidity and impact resistance. Since the invention of a stereospecific catalyst by Ziegler and Natta, crystalline polyolefins have been used as general-purpose resins of superior performance and their production has increased throughout the world in recent years because of their outstanding rigidity, heat resistance, and lightness in weight. However, due to a disadvantage of being brittle at low temperatures, crystalline polypropylene is not suitable for applications that require impact resistacne at low temperatures. To remedy this disadvantage, a great deal of study has been made and there are proposed many methods for improvement. Industrially useful methods among them include the block copolymerization of propylene and other olefins, particularly ethylene, as disclosed in Japanese Patent Publication Nos. 38-14834 (1963), 39-1836 (1964), and 39-15535 (1964). These methods, however, suffer from a disadvantage that the resulting block copolymer is poorer in rigidity and transparency than crystalline polypropylene and the moldings produced therefrom are liable to whitening on bending and impact deformation. To solve this problem, there was proposed a method for carrying out block copolymerization in three stages, a disclosed in Japanese Patent Publication Nos. 44-20621 (1969) and 49-24593 (1974). These methods result in block copolymers having outstanding physical properties. According to these methods, copolymerization is performed in an inert solvent such as n-heptane using a catalyst of comparatively low activity, in which case the inert solvent has to be recovered, an extremely complex post-treatment is required, and a considerably large portion of polymer is soluble in the inert solvent. These factors lead to the great increase of poduction cost. On the other hand, there were proposed in Japanese Patent Publication No. 42-17488 (1967) and Japanese Laid-open Patent Nos. 49-120986 (1974) and 52-3684 (1977) methods for producing block copolymers by bulk polymerization or gas-phase polymerization in which the recovery of inert solvent is comparatively easy or is not virtually required, or virtually no inert solvent is employed. According to these methods, virtually no inert solvent is used, and consequently the solvent purification step is omitted and the drying of polymer is simplified to a great extent. Nevertheless, the step for removing catalyst residues is required because the catalyst employed is not sufficient in activity. Moreover, in bulk polymerization and gas-phase polymerization, it is difficult to remove polymers of low molecular weight and low crystallinity, and this deteriorates the properties of the resulting polymer and increases the viscosity of the resulting polymer, making the handling of the polymer inconvenient. There is known another method for producing propylene-ethylene block copolymer continuously to increase the productivity per unit time and per unit volume of polymerization reactor. A continuous process often involves problems which are not encountered in batch-wise process. This is particularly true in the production of block copolymers. In order to impart desired properties as mentioned above to the polymer, it is necessary to provide several reaction stages in which the ethylene/propylene reaction ratio is different. If block copolymers of many kinds are to be produced, it is necessary to install as many reaction vessels as the reaction stages. In multi-stage polymerization using a series of reaction vessels, the quantity of polymerization per unit weight of catalyst varies from one reaction vessel to another. Therefore, the resulting polymers are quite different in the properties depending on whether the polymers are produced by a batch-wise process or continuous process. In bulk polymerization in which propylene per se is used as a liquid medium, the following reaction vessel is increased in pressure in order to increase the ethylene/propylene reaction rate in the following-stage. Such arrangements make it necessary to transfer by pressure the slurry from the low pressure side to the high pressure side. Such a step requires an expensive equipment and involes a danger of line clogging with molten polymers.